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Global exponential stability of BAM neural networks with delays and impulses. (English) Zbl 1099.68085

Summary: Sufficient conditions are obtained for the existence and global exponential stability of a unique equilibrium of a class of two-layer heteroassociative networks called bidirectional associative memory (BAM) networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. An illustrative example is given to demonstrate the effectiveness of the obtained results.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
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[1] Hopfield, J. J., Neuron with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. USA, 81, 3088-3092 (1984) · Zbl 1371.92015
[2] Kosto, B., Bi-directional associative memories, IEEE Trans. Syst. Man. Cybernet, 18, 49-60 (1988)
[3] Gopalsamy, K.; He, X. Z., Delay-independent stability in bi-directional associative memory networks, IEEE Trans. Neural Networks, 5, 998-1002 (1994)
[4] Kelly, D. G., Stability in contractive nonlinear neural networks, IEEE Trans. Biomed. Eng., 37, 231-242 (1990)
[5] Liao, X. F.; Yu, J. B., Qualitative analysis of bidrectional associative memory with time delays, Int. J. Circuit Theory Appl., 26, 219-229 (1998)
[6] Liao, X. X., Stability of the Hopfield neural networks, Sci. China, 23, 5, 523-532 (1993)
[7] Rao, V. S.H.; Phaneendra, B. R.M., Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones, Neural networks, 12, 455-465 (1999)
[8] Zhao, H., Global stability of bidirectional associative memory neural networks with distributed delays, Phys. Lett. A, 297, 182-190 (2002) · Zbl 0995.92002
[9] Liang, J.; Cao, J., Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays, Chaos, Solitons & Fractals, 22, 773-785 (2004) · Zbl 1062.68102
[10] Guan, Z.; Chen, G.; Qin, Y., On equilibria, stability and instability of Hopfield neural networks, IEEE Trans. Neural Networks, 2, 534-540 (2000)
[11] Guan, Z. H.; James, L.; Chen, G., On impulsive auto-associative neural networks, Neural Networks, 13, 63-69 (2000)
[12] Akca¸, H.; Alassar, R.; Covachev, V.; Covacheva, Z.; Al-Zahrani, E., Continuous-time additive Hopfield-type neural networks with impulses, J. Math. Anal. Appl., 290, 436-451 (2004) · Zbl 1057.68083
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